That animals convert grass and plants in general to meat is undeniable. But I think the issue is, livestock is generally fed with human grown plants, which could be fed directly to humans and save a lot of energy (food and water) wasted in the process, because the amount of calories, for example, that you take off meat is nowhere near the calories contained in the food the animal consumed during its lifetime. Now, regarding if nutrients are missing from a plants only diet, that's another matter.

the quantity of animals is way too high for them to be fed with grass, as that would turn into a logistical nightmare.

It's usually a special feed, which is composed of corn, often bones and other substances.